论文标题
关于JKO-SCHEME的收敛和对多种趋化系统的解决方案的爆炸，没有质量保存
On the Convergence of the JKO-scheme and Blow-up of solutions for a Multi-species Chemotaxis System with no Mass Preservation
论文作者
论文摘要
这项工作考虑了包括出生或死亡率术语的多种物种的趋化系统，这意味着没有大量保存人群。我们的目的是表明与[35,14]精神的最佳运输理论产生的JKO-方案的局部时间，即局部时间，是局部时间，即局部时间，这是局部时间的融合。当前，$ l^{\ infty} $解决方案已证明对获得独特性很重要。由于死亡率案例不能确保全球解决方案对于任意初始数据，因此在此框架中，分析该系统的爆炸现象可能是兴趣。因此，在最后一部分中，我们得到了足够的条件，意味着在有限的时间内爆炸现象，并在发生这种情况的几个阶段。最后一部分可以看作是[16]中爆破结果的部分概括。
This work considers a chemotaxis system for multi-species that includes birth or death rate terms, which implies no mass preservation of the populations. We aim to show the convergence to a $L^{\infty}\ -\ $weak solutions, that is local in time, of the JKO - scheme arising from the Optimal Transport Theory, in the spirit of [35,14]. Currently, $L^{\infty}$ solutions have shown to be important in order to get uniqueness. Since death rate case does not ensure global solutions, for arbitrary initial data, in this framework, it could be interest to analyze the Blowing-up phenomenon of this system. Therefore, in the last section, we get sufficient conditions that implies blowing-up phenomenon in finite time and we draw several stages where this occurs. This last part can be seen as a partial generalization of the blowing-up results in [16].
